Simplified and symmetrical five-bar linkage driver for manipulating a Six-Degree-of-Freedom Parallel &#34;minimanipulator&#34; with three inextensible limbs

ABSTRACT

A Six-Degree-of-Freedom Parallel-Manipulator having three inextensible limbs for manipulating a platform is described in which the three inextensible limbs are attached via universal joints to the platform at non-collinear points. Each of the inextensible limbs is also attached via universal joints to a two-degree-of-freedom parallel driver such as a five-bar lineage, a pantograph, or a bidirectional linear stepper motor. The drivers move the lower ends of the limbs parallel to a fixed base and thereby provide manipulation of the platform. The actuators are mounted on the fixed base without using any power transmission devices such as gears or belts.

ORIGIN OF THE INVENTION

The invention described herein was jointly made by an employee of theUnited States Government and a non-employee of the United StatesGovernment. This invention may be manufactured and used by or for theGovernment for governmental purposes without the payment of anyroyalties thereon or therefor.

This is a division of application Ser. No. 07/915,567, filed Jul. 20,1992.

TECHNICAL FIELD

This invention relates to manipulators in general and in particular to a"minimanipulator" designed to provide high resolution and high stiffnessfor fine position and force control in a hybrid serial-parallelmanipulator system.

BACKGROUND ART

Flight simulators such as the Stewart platform (Stewart, D. 1965, "APlatform with Six Degrees of Freedom," Proc. Institute of MechanicalEngr., London, England, Vol. 180, pp. 371-386) have been used andstudied as parallel manipulators. Kohli et al. (Kohli, D., Lee, S. H.,Tsai, K. Y., and Sandor, G. N., 1988, "Manipulator Configurations Basedon Rotary-Linear (R-L) Actuators and Their Direct and InverseKinematics," Trans. ASME, J. of Mech., Transmis., and Auto. in Design,Vol. 110, pp. 397-404) studied six-degree-of-freedom (six-DOF) parallelmanipulators which are driven by base-mounted Rotary-Linear actuators.Hudgens and Tesar (Hudgens, J. C., and Tesar, D., 1988, "AFully-Parallel Six Degree-of-Freedom Micromanipulator: KinematicAnalysis and Dynamic Model," Trends and Developments in Mechanisms,Machines, and Robotics--Proc. of the 20th Biennial MechanismsConference, ASME, New York, DE--Vol. 15-3, pp. 29-37) introduced a newsix-DOF parallel micromanipulator suitable for serial-parallel systems.Pierrot et al. (Pierrot, F., Fournier, A., and Dauchez, P., 1991,"Towards a Fully-Parallel 6 DOF Robot for High-Speed Applications,"Proc. of the 1991 IEEE International Conference on Robotics andAutomation, pp. 1288-1293) introduced a high-speed six-DOF parallelmanipulator.

DISADVANTAGES OF PRIOR ART

Most of the six-DOF parallel manipulators which have been proposed inthe past contain six limbs. The Stewart platform, the manipulatorintroduced by Hudgens and Tesar, and the mechanism studied by Pierrot etal. all contain six limbs. Compared to a three-limbed parallelmechanism, such as the present invention,

1. Their direct kinematics analyses are very complicated.

2. There is a higher possibility of mechanical interference betweentheir limbs.

3. More parts are needed in their construction.

Note that the only six-limbed, six-DOF parallel manipulators for whichclosed-form direct kinematics solution has been reported in theliterature are special forms of the Stewart platform (Nanua, P.,Waldron, K. J., and Murthy, V., 1990, "Direct Kinematic Solution of aStewart Platform," IEEE Transactions on Robotics and Automation, Vol. 6,pp. 438-444; Griffis, M., and Duffy, J., 1989, "A Forward DisplacementAnalysis of a Class of Stewart Platforms," J. of Robotic Systems, Vol.6, pp. 703-720; Innocenti, C., and Parenti-Castelli, V., 1990, "DirectPosition Analysis of the Stewart Platform Mechanism," Mechanism andMachine Theory, Vol. 25, pp. 611-612), In these special forms, pairs ofspherical joints are concentric on either the platform or both the baseand the platform. However, as mentioned by Griffs and Duffy, pairs ofconcentric spherical joints may very well present design problems.

In a Stewart platform, if the prismatic joints are actuated by electricpower, then the actuators are not fixed. As a result, the weight of eachactuator is a load for the other actuators. As a result

1. Payload capacity is reduced.

2. Actuator sizes are increased.

3. More power is dissipated.

The limbs in the Stewart platform and the mechanisms introduced by Kohliet al. and Pierrot et al. are extensible (each limb contains a revoluteor a prismatic joint). As a result, their resolutions, accuracies andstiffness properties are worse than those of the present invention.

ADVANTAGES OF THE PRESENT INVENTION OVER THE PRIOR ART

Compared to the prior art six-limbed, six-DOF parallel manipulators(Stewart; Hudgens and Tesar; Pierrot et al., etc.), a "minimanipulator"has the following advantages:

1. Closed-form solution can be obtained for its direct kinematics(Tahmasebi, F., and Tsai, L. W., 1992, "Closed-Form Direct KinematicsSolution of a New Parallel Minimanipulator," Accepted for presentationat the 1992 Japan-U.S.A. Symposium on Flexible Automation).

2. There is a lower possibility of mechanical interference between itslimbs

3. Fewer number of parts are needed in its construction.

Compared to the prior art six-DOF parallel mechanisms with movingactuators, a "minimanipulator" has the following advantages:

1. Its payload capacity can be made higher.

2. Its actuators can be made smaller.

3. It dissipates less power.

Inextensible limbs and two-DOF drivers of a "minimanipulator" increaseits positional resolution and stiffness (Tahmasebi, F., and Tsai, L. W.,1992, "Jacobian and Stiffness Analysis of a Novel Class of Six-DOFParallel Minimanipulators," Accepted for presentation at the 22ndBiennial Mechanisms Conference).

Statement of the Invention

It is therefore an object of the present invention to provide a six-DOFparallel manipulator that has superior resolution, accuracy, andstiffness as compared to the prior art.

Another object of the present invention is to mount all of its actuatorson its fixed base without using any power transmission devices (e.g.,gears, belts).

A further object of the present invention is to use the minimum possiblenumber of limbs in its synthesis.

A still further objective of the present invention is to have symmetrybetween its limbs.

These and other objects are achieved by providing a Six-DOF Parallel"Minimanipulator" with three inextensible limbs. The term"minimanipulator" is used because this mechanism is not designed toprovide very large platform displacements. To provide high resolution,accuracy, and stiffness, the present invention is designed to haveinextensible limbs. The Lower end of each limb is connected to a two-DOFdriver (e.g., a bidirectional linear stepper motor, an X-Y positiontable, a pantograph or a five-bar linkage) and can be moved freely onthe base plate. The desired "minimanipulator" motion is obtained whenthe drivers move the lower ends of its three limbs on its base plate.Pantograph or five-bar linkage drivers further improve resolution,accuracy, and stiffness of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a representation of an inextensible limb connected to aplatform and a base.

FIG. 2 is a kinematic equivalent of the limb represented by FIG. 1.

FIG. 3 is a representation of a "minimanipulator".

FIG. 4 represents pantographs as two-DOF drivers for the"minimanipulator" of FIG. 3.

FIG. 5 represents five-bar linkages as two-DOF drivers for the"minimanipulator" of FIG. 3.

FIG. 6 is a simplified version of the five-bar linkage driver of FIG. 5.

FIG. 7 shows the minimanipulator driven by bidirectional linear steppermotors or X-Y position tables mounted to the base member.

FIG. 8 shows in detail the simplified five-bar linkage drier of FIG. 6.

FIG. 9 shows the simplified five-bar linkage driver of FIG. 8 connectedto one leg of the "minimanipulator".

DETAILED DESCRIPTION OF THE INVENTION

As mentioned above in the section entitled Disadvantages of Prior Art,many of the prior art six-DOF parallel mechanisms described in theliterature contain six limbs. Reducing the number of limbs in a parallelmechanism lowers the number of loops in its structure. As a result,direct kinematics of the mechanism is simplified whereas its inversekinematics becomes more challenging. Since direct kinematics of aparallel manipulator is much more difficult than its inverse kinematics,the present invention, a Three-Limbed Six-Degree-of-Freedom Parallel"Minimanipulator" is designed to contain a minimum number of limbs.Minimizing the number of limbs results in numerous benefits, namely:lower number of links and joints, lower "minimanipulator" weight, andhigher dexterity. Three non-collinear points on a platform of a six-DOFparallel manipulator will completely define its location (position andorientation) in space. Therefore, each "minimanipulator" contains threelimbs which connect three non-collinear points on its platform to itsbase.

For the reasons mentioned in the section entitled Disadvantages of PriorArt, the present invention is designed to have base-mounted actuatorsand inextensible limbs. The actuators are mounted on the base withoutusing any power transmission devices such as belts or gear trains. Dueto friction and backlash, power transmission devices introduce lowstiffness and accuracy problems. In addition, the limbs are alsosymmetric (a symmetric six-DOF parallel manipulator is defined as havingidentical joints and links in each limb connecting its base to itsplatform). Symmetry is needed for an even load distribution. The Lowerend of each limb is connected to a two-DOF driver (e.g., a bidirectionallinear stepper motor, an X-Y position table, a pantograph or a five-barlinkage) and can be moved freely on the base plate. The desired"minimanipulator" motion is obtained when drivers move the lower ends ofits three limbs parallel to its base plate. Each limb of the symmetricsix-DOF parallel "minimanipulator" must have six degrees of freedom inits joints; the proof of this is as follows:

    ______________________________________                                        Symbol    Description                                                         ______________________________________                                        f.sub.k   degrees of freedom of joint k                                       F         degrees of freedom of a parallel manipulator                        j         number of joints in each limb                                       J         total number of joints in a parallel manipulator                    k         index                                                               m         number of limbs in a parallel manipulator                           n         number of links in each limb                                        N         total number of links in a parallel manipulator                     λ  integer, 3 for planar & spherical mechanisms,                                 6 for spatial mechanisms                                            σ   total degrees of freedom in joints of each limb                     ______________________________________                                    

Each limb is an open kinematic chain which connects the base to theplatform. Let j include the top and bottom joints which connect a limbto the platform and the base. Then

    j=n+1

Total number of links and joints in a parallel manipulator are relatedto number of links and joints in each limb by the followingrelationships:

    N+mn+2

    J=mj

Number of DOF of a mechanism can be obtained from the following mobilityequation: ##EQU1## For a six-DOF symmetric parallel manipulator, F=6,λ=6, and ##EQU2## Therefore, the mobility equation reduces to:

    6=6[mn+2-m(n+1)-1]+mo

After simplification, the intended result is obtained. That is:

    σ=6

Therefore, in addition to the two-DOF provided by a driver, each limbshould be given four more DOF. To keep the limbs inextensible, jointsare placed only at their lower and upper ends. A three-DOF sphericaljoint at one end and a revolute joint at the other end can be used.However due to difficulties in their fabrication, spherical joints arenot very precise. Hence, they are not recommended for the"minimanipulators". Instead, a two-DOF universal joint is placed at eachend of a limb, as shown in FIG. 1. One of the axes of upper universaljoint 2 is collinear with limb 6_(i) (subscript i represents numbers 1,2, and 3 in a cyclic manner); while the other axis of upper universaljoint 2, as well as one of the axes of lower universal joint 4, arealways perpendicular to limb 6_(i). The platform is shown as item 12.This arrangement is kinematically equivalent to a limb with a sphericaljoint 8 at its lower end and a revolute joint 10 at its upper end, asshown in FIG. 2. Note that by using the limb configuration shown in FIG.1, the kinematics of the "minimanipulator" is made independent of theoutput link orientations of its two-DOF drivers. Due to simplicity ofits representation, the equivalent limb configuration shown in FIG. 2has been used in kinematics analysis of the "minimanipulators".

A representation of a complete "minimanipulator" is shown in FIG. 3.Points R₁, R₂ and R₃ are connected to two-DOF drivers (described later)and can be moved on a base plate (to be shown later). Points P₁, P₂ andP₃ are on platform 12. To keep the "minimanipulator" geometricallysymmetric, axes of the topmost revolute joints at points P₁, P₂ and P₃are made parallel to lines P₂ P₃, P₃ P₁, and P₁ P₂ respectively.

Two-DOF planar mechanisms (e.g., bidirectional linear stepper motors,X-Y position tables, pantographs and five-bar linkages) are used atpoints R₁, R₂, R₃ as drivers. Pantographs and five bar linkages arecapable of increasing the mechanical advantage of the "minimanipulator".As a result, better positional resolution and stiffness can be obtained.

PANTOGRAPHS AS TWO-DOF DRIVERS

Pantograpbs are often used for magnifying displacement and speed (e.g.,Song, S. M., Waldron, K. J., and Kinzel, G. L., 1985, "Computer-AidedGeometric Design of Legs for a Walking Vehicle," Mechanism and MachineTheory, Vol. 20, pp. 587-596). In the present invention, they are usedas speed-reduction devices. FIG. 4 shows a completely symmetricalarrangement of three simple pantographs 20₁, 20₂, and 20₃, mounted onbase 24, which can be used to drive the six-DOF parallel"minimanipulator". Points C₁, C₂, and C₃ are the output points of thepantographs 20₁, 20₂, and 20₃ and are connected to limbs 6₁, 6₂, and 6₃(see FIG. 3). The desired platform 12 motion is obtained by drivingsliders A₁, A₂, A₃ and B₁, B₂, B₃ inside guides 22.

Motion can be illustrated as follows: subscript i represents numbers 1,2, and 3 in a cyclic manner. There are revolute joints at points A_(i),B_(i), C_(i), D_(i), E_(i) and F_(i). Prismatic joints connect slidersA_(i) and B_(i) to guides 22. Point C_(i) always lies on line A_(i)B_(i). If slider B_(i) is fixed and slider A_(i) is moving, a similarpath is followed by the output point C_(i) with a reduction factor ofR_(a),i. Likewise, if slider A_(i) is fixed and slider B_(i) is moving,a similar path is followed by the output point C_(i) with a reductionfactor of R_(b),i. These reduction factors are equal to the followingratios: ##EQU3##

The above results are based on derivations presented by Song etal.(1985). When both sliders A_(i) and B_(i) are moving, the resultantdisplacement of the output point C_(i) is the vector sum of thedisplacements described above. Such displacement reductions areequivalent to reduction in speed or increase in mechanical advantage. Asa result, stiffness and positional resolution of the "minimanipulator"is improved.

Motions generated at the output point C_(i) by sliders A_(i) and B_(i)are decoupled. As mentioned by Song et al. (1985) the decoupling featureof pantographs provides simpler coordination control and better energyefficiency. However, the above equations for the reduction factors showthat:

    R.sub.a,i +R.sub.b,i =1

Such reduction factors may not be good enough for applications whichrequire very high resolution and stiffness. Therefore, five-bar linkagesare also available for speed reduction in the "minimanipulators" andwill be discussed in the next section.

Skew pantographs are not advisable because, in an arrangement similar tothe one described above, they do not reduce speeds as well as simplepantographs do (sum of the speed reduction factors for a skew pantographis greater than one). In addition, in a skew pantograph, the path of theoutput point is rotated with respect to the slider paths. Such rotationscomplicate the calculations needed for control of a "minimanipulator".

FIVE-BAR LINKAGES AS TWO-DOF DRIVERS

Five-bar linkages have been used by Asada and Ro (Asada, H., and Ro, I.H., 1985, "A Linkage Design for Direct-Drive Arms,", Trans. ASME, J. ofMech., Transmis., and Auto. in Design. Vol. 107, pp. 536-540) to improveforce and speed characteristics of two-DOF direct-drive robot arms.Bajpai and Roth (Bajpai, A., and Roth, B., 1986, "Workspace and Mobilityof a Closed-Loop Manipulator," The International J. of RoboticsResearch, Vol. 5, pp. 131-142) have studied workspace and mobility ofmanipulators with structures based on five-bar linkages. In the presentinvention, two five-bar linkage configurations are shown which aresuitable for improving resolution and stiffness of the"minimanipulators".

FIG. 5 shows three identical five-bar linkages 30₁, 30₂ and 30₃ mountedon base 32 which can be used to drive the "minimanipulator". Points C₁,C₂ and C₃ are the output points of the five-bar linkages (see FIG. 1).Base-mounted rotary actuators 40 are placed at points G₁, G₂, G₃ and H₁,H₂, H₃. Asada and Ro (1985) showed that the larger the speed reductionat the output point of a five-bar linkage, the smaller the workspacewhich can be generated. They also illustrated that the smaller the inputlink lengths (H_(i) J_(i) and G_(i) I_(i)) with respect to the otherlink lengths (J_(i) C_(i) and I_(i) C_(i)), the higher the speedreduction at the output point C_(i). The lower end of a manipulator limbis not required to move over a large area on a base plate. Hence, thefive-bar linkages are designed to provide large speed reductions attheir output points (i.e., their input links are made much smaller thantheir other links).

SIMPLIFIED FIVE-BAR LINKAGES AS TWO-DOF DRIVERS

The driving five-bar linkages can be simplified by making the axes ofrotary actuators G_(i) and H_(i) (see FIG. 5) coincide, as shown in FIG.6. At point K₁, K₂, K₃, there is an actuator 40 on each side of base 32to drive links K_(i) J and KI. The simplified five-bar drivers which areconsidered here are completely symmetric. That is: ##EQU4## As a result,coordination between actuator rotations can be easily accomplished.Namely, angular displacement of an output point C_(i) is obtained byequal actuator rotations, and its radial displacement is obtained byequal and opposite actuator rotations.

OTHER TWO-DOF DRIVERS

Bidirectional linear stepper motors (Yeaple, F., 1988, "ChoreographedRobots Insert Automotive Parts," Design News, Vol. 44, No. 21, pp.134-135) or X-Y positioning tables can also be used to move the lowerend of limb 6 on base 32. See FIG. 7 where the bidirectional linearstepper motors and the X-Y positioning tables are shown as elements 50.However, such devices do not provide any increase in mechanicaladvantage of the "minimanipulator". Note that a bidirectional linearstepper motor acts as a X-Y positioning table, but its stators arebase-mounted.

RECOMMENDED DRIVERS

A five-bar linkage, like that shown in FIG. 5, has fewer links than apantograph. In addition, all of the joints in a five-bar linkage arerevolute which can be designed and maintained easier than prismaticjoints. As mentioned earlier, a five-bar linkage can be designed toprovide a higher speed reduction than a pantograph. On the other hand,the decoupling feature of a pantograph results in better coordinationcontrol and energy efficiency. However, the simplified Five-Barconfiguration shown in FIG. 6 can also provide simple coordinationcontrol. Hence, it may be more suitable than those configurations shownin FIGS. 4 and 5 for many applications.

ALTERNATIVE EMBODIMENTS OF THE INVENTION

The two-DOF drivers can be designed to obtain larger workspace withreduced resolution and stiffness. For example, if simplified five-bardrivers are used (see FIG. 6), the workspace can be maximized by makingK_(i) Ii equal to I_(i) C_(i) and K_(i) J_(i) equal to J_(i) C_(i). Aparallel mechanism with the same structure as the "minimanipulator" andwith a larger workspace can be used as a motion simulator. In addition,a "minimanipulator" can be used as a passive compliant device or aforce/torque sensor, if its actuators are replaced by rotationaldisplacement transducers.

To those skilled in the art, many modifications and variations of thepresent invention are possible in light of the above teachings. It istherefore to be understood that the present invention can be practicedotherwise than as specifically described herein and still will be withinthe spirit and scope of the appended claims.

I claim:
 1. A six-degree-of-freedom parallel manipulator comprising:three inextensible limbs each having a first end and a second end; each of said inextensible limbs moveably attached at said first end to a platform at non-collinear points on said platform; and three simplified five-bar linkage planar driver means affixed to a base member and moveably attached to each said second end of said inextensible limbs for providing planar movement to each said second end of each said inextensible limb thereby providing manipulation of said platform; each said simplified five-bar linkage planar driver means having two coaxial rotary actuators as driving means for each said five-bar linkage planar driver means.
 2. The device of claim 1 wherein each of said inextensible limbs are moveably attached at each end with joints such that each limb is provided with six degrees of freedom.
 3. The device of claim 2 wherein each said limb has a three-degree-of-freedom spherical joint at said second end and a revolute joint at said first end.
 4. The device of claim 2 wherein each said limb has a two-degree-of-freedom universal joint at each end.
 5. The device of claim 4 wherein one of the axes of the universal joint at said first end is collinear with its limb, and the other axes of the universal joint at said first end as well as one axes of the universal joint at said second end are perpendicular to its limb.
 6. The device of claim 1 wherein each said simplified five-bar linkage planar driver means is arranged as a speed reduction five bar linkage.
 7. A simplified five-bar linkage for manipulating robotic limbs comprising:a first rotary actuator having a first link connected thereto at one end of said first link; a second rotary actuator having a second link connected thereto at one end of said second link; a third link connected at one end to the other end of said first link; a fourth link connected at one end to the other end of said second link; said third and fourth links connected at their ends not connected to said first and second links thereby forming an output point; said first and second rotary actuators being coaxial.
 8. The simplified five-bar linkage of claim 7 wherein the length of said first link is equal to the length of said second link.
 9. The simplified five-bar linkage of claim 8 wherein the length of said third link is equal to the length of said fourth link.
 10. The simplified five-bar linkage of claim 7 wherein said four links are equal in length. 